Geodesic
On the Existence of $L_2$ Boundary Values of Solutions to an Elliptic Equation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 56-74

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The behavior of solutions of a second-order elliptic equation near a distinguished piece of the boundary is studied. On the remaining part of the boundary, the solutions are assumed to satisfy the homogeneous Dirichlet conditions. A necessary and sufficient condition is established for the existence of an $L_2$ boundary value on the distinguished part of the boundary. Under the conditions of this criterion, estimates for the nontangential maximal function of the solution hold, the solution belongs to the space of $(n-1)$-dimensionally continuous functions, and the boundary value is taken in a much stronger sense.
Mots-clés : elliptic equation
Keywords: boundary value, Dirichlet problem. 
@article{TM_2019_306_a5,
     author = {A. K. Gushchin},
     title = {On the {Existence} of $L_2$ {Boundary} {Values} of {Solutions} to an {Elliptic} {Equation}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {56--74},
     publisher = {mathdoc},
     volume = {306},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_306_a5/}
}
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A. K. Gushchin. On the Existence of $L_2$ Boundary Values of Solutions to an Elliptic Equation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 56-74. http://geodesic.mathdoc.fr/item/TM_2019_306_a5/